I honestly don't know the true answer to this, but I do believe that most of our founding fathers didn't want this to be a Christian nation. If they had wanted this, I don't see why they didn't put something to that affect in the Constitution. (And, no, I don't believe that references to God in any government document prove that they wanted religion to be part of our government, but rather that is the only thing they knew at the time, for the most part.)
What I do know is that in the last 200 years we have advanced our own knowledge and learned many things, including a lot about biology and human behavior that they didn't. Then, a country ruled by its people was a new concept, rarely, if ever, done to the extent that they took it. They incorporated as many concepts about individual freedoms and how to protect them and trying to ensure that the people would be the ones to rule their leaders as they knew and could get support for at that time. Now, such a concept is considered completely normal and it is the goal of many countries to attain this state, most countries that aren't "third world countries" with a few exceptions. And we have come to realize through those 2+ centuries that there are even more ways to attain individual freedoms and to ensure that everyone's views are able to be expressed while still trying to ensure that everyone is treated fairly. The system doesn't always work, and there certainly are going to be times when individual freedoms clash, with others and/or with what the government feels they must do, but that is no reason to allow what direction the founding fathers might have wanted this country to go in (although, it is most likely that none of them agreed completely on this anyway) but didn't include into the Constitution, to dictate where we should take this country. Some of the things that it is obvious that the founding fathers did agree on was individual freedom to the extent that it doesn't violate another person's is important, which is exemplified in the Bill of Rights.